Five standard tests are compared: chi-squared, Fisher's exact, Yates’ correction, Fisher’s exact mid-p, and Barnard’s. Yates’ is always inferior to Fisher’s exact. Fisher’s exact is so conservative that one should look for alternatives. For certain sample sizes, Fisher’s mid-p or Barnard’s test maintain the nominal alpha and have superior power.
Hasselblad, Vic and Lokhnygina, Yulia
"Tests for 2 x 2 Tables in Clinical Trials,"
Journal of Modern Applied Statistical Methods:
2, Article 10.
Available at: http://digitalcommons.wayne.edu/jmasm/vol6/iss2/10